The argument from ignorance (or argumentum ad ignorantiam and negative proof) is a logical fallacy that claims the truth of a premise is based on the fact that it has not (yet) been proven false, or that a premise is false because it has not (yet) been proven true. This is often phrased as "absence of evidence is not evidence of absence".

If the only evidence for something's existence is a lack of evidence for it not existing, then the default position is one of mild skepticism and not credulity. This type of negative proof is common in proofs of God's existence or in pseudosciences where it is used as an attempt to shift the burden of proof onto the skeptic rather than the proponent of the idea. The burden of proof is on the individual proposing existence, not the one questioning existence.

Another form that this fallacy can take is the form that of an argument from incredulity (also known as argument from personal belief or argument from personal conviction) which is that one's personal incredulity or credulity towards a premise is a logical reason for acceptance or rejection. This incredulity can stem from ignorance (defined as a lack of knowledge and experience) or from willful ignorance (defined as a flat out refusal to gain the knowledge). The concept of irreducible complexity is based entirely around this idea of personal incredulity. One person (Michael Behe) cannot see how something evolved naturally, therefore it can't possibly evolve naturally.

Almost all the claims from the anti-science movement revolve around some form of personal incredulity or argument from ignorance.

Proponents of the anti-science movement will usually pick some aspect of a currently accepted scientific theory and argue that it must be wrong because they do not believe it explains some aspect of the natural world. Common examples of this are such claims as "you can't prove global warming is caused by humans," "I don't see how evolution could increase the complexity of an organism," "material properties of the brain cannot presently explicitly explain consciousness so it must be caused by non-materialist processes," or "I don't know how this alternative medicine works, but it does."

“”Ignorance is ignorance; no right to believe anything can be derived from it. In other matters no sensible person will behave so irresponsibly or rest content with such feeble grounds for his opinions and for the line he takes.

A common retort to a negative proof is to reference the existence of the Invisible Pink Unicorn or the Flying Spaghetti Monster as just as valid as the proposed entity of the debate. This is similar to reductio ad absurdum, that taking negative proof as legitimate means that one can prove practically anything, regardless of how absurd.

A religious apologist using the argument from ignorance would state something like, "the existence of God is true because there is no proof that the existence of God is false". But a counter-apologist can use that same "argument" to state, "the nonexistence of God is true because there is no proof that the nonexistence of God is false". This immediately demonstrates how absurd the argument from ignorance is by turning the tables on those who use this "argument" fallacy, like some religious apologists.

One important element to remember in regards to negative proof is that once positive evidence has been presented the burden shifts to the skeptic to refute the evidence presented. One cannot keep arguing from the position of "negative proof" after the presentation of valid evidence. This point, however, is completely lost on most creationists (such as intelligent design advocates) who shout from the rooftops that there are no transitional fossils long after they've been repeatedly shown them. Confirmation bias, anyone?

A common saying in pseudologic is "You can't prove a negative." This is, as the hatnote up top says, simply not true. This is clearly not true because any statement can be rewritten into the negation of its negation. Any provable statement can be written as a negative. For example, "X is true" can be rewritten as "X is not false", a negative statement! If "X is true" can be proven true, then you have also proven a negative statement "X is not false".